Method to Design Expandable Cement Based upon Specified Downhole Conditions

ABSTRACT

A method of performing a cementing operation with an expandable cement deployable into a wellbore penetrating a subterranean formation is provided. The method involves determining design parameters of a wellsite, determining at least one estimated eigenstrain of the expandable cement based on the design parameters, selecting the expandable cement based on the estimated eigenstrain, and validating the selected expandable cement by comparing the estimated eigenstrain with the empirical eigenstrain. The design parameters includes a minimum pre-stress of the wellbore sufficient to prevent creation of a microannulus in the wellbore. The estimated eigenstrain is sufficient to generate the determined minimum pre-stress.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of European Patent Application No. EP 14305462.5, filed on Mar. 31, 2014, which is incorporated herein by reference in its entirety.

BACKGROUND

The present disclosure relates generally to techniques for performing wellsite operations. More specifically, the present invention relates to cement (e.g., expandable cement) usable in wellbore operations, such as completions.

Hydrocarbons may be produced by drilling wellbores and deploying tools downhole to reach subsurface reservoirs. Once drilled, the wellbore may be completed in preparation for production. The well is completed by inserting a steel casing into the wellbore and securing the casing into place with a wellbore cement.

Wellbore cement may be pumped into the wellbore to line the wellbore wall. The cement may be used to support the casing and to provide zonal isolation along the wellbore. The cement may be made of a slurry and additives. Examples of cements and/or related techniques are provided in Patent/Application Nos. WO01/66487, US 20110193564, U.S. Pat. No. 8,531,189 and U.S. Pat. No. 6,817,238, the entire contents of which are hereby incorporated by reference herein.

SUMMARY

In at least one aspect, the disclosure relates to a method of performing a cementing operation with an expandable cement deployable into a wellbore penetrating a subterranean formation. The method involves determining design parameters of a wellsite, determining at least one estimated eigenstrain of the expandable cement based on the design parameters, selecting the expandable cement based on the at least one estimated eigenstrain, and validating the selected expandable cement by comparing the at least one estimated eigenstrain with the at least one empirical eigenstrain. The design parameters include a minimum pre-stress of the wellbore sufficient to prevent creation of a microannulus in the wellbore. The estimated eigenstrain is sufficient to generate the determined minimum pre-stress.

In another aspect, the disclosure relates to a method of performing a cementing operation with an expandable cement deployable into a wellbore penetrating a subterranean formation. The method involves designing an expandable cement for cementing the wellbore and cementing the wellbore with the designed expandable cement. The designing involves determining design parameters of a wellsite, determining at least one estimated eigenstrain of the expandable cement based on the design parameters, selecting the expandable cement based on the at least one estimated eigenstrain, and validating the selected expandable cement by comparing the at least one estimated eigenstrain with the at least one empirical eigenstrain. The design parameters include a minimum pre-stress of the wellbore sufficient to prevent creation of a microannulus in the wellbore. The estimated eigenstrain is sufficient to generate the determined minimum pre-stress.

Finally, in another aspect, the disclosure relates to a method of performing a cementing operation with an expandable cement deployable into a wellbore penetrating a subterranean formation. The method involves measuring at least one empirical eigenstrain of at least one expandable cement with at least one cement expansion apparatus and designing an expandable cement for cementing the wellbore. The designing involves determining design parameters of a wellsite, determining at least one estimated eigenstrain of the expandable cement based on the design parameters, selecting the expandable cement based on the at least one estimated eigenstrain, and validating the selected expandable cement by comparing the at least one estimated eigenstrain with the at least one empirical eigenstrain. The design parameters include a minimum pre-stress of the wellbore sufficient to prevent creation of a microannulus in the wellbore. The estimated eigenstrain is sufficient to generate the determined minimum pre-stress.

BRIEF DESCRIPTION DRAWINGS

So that the above recited features and advantages can be understood in detail, a more particular description, briefly summarized above, may be had by reference to the embodiments thereof that are illustrated in the appended drawings. It is to be noted, however, that the appended drawings illustrate only typical embodiments and are, therefore, not to be considered limiting of its scope. The figures are not necessarily to scale and certain features and certain views of the figures may be shown exaggerated in scale or in schematic in the interest of clarity and conciseness.

FIGS. 1A and 1B illustrate schematic views of a wellsite with a drilled and a cased wellbore, respectively, in accordance with an embodiment of the disclosure, the wellsite including wellsite equipment and a surface unit having a cement design tool;

FIGS. 2A and 2B illustrate a schematic view of an unconfined expansion tester in an operational configuration and an open position, respectively, in accordance with an embodiment of the disclosure;

FIGS. 3A and 3B illustrate a schematic view of a confined expansion tester in an operational configuration and in an open position, respectively, in accordance with an embodiment of the disclosure;

FIG. 4 is a flow chart depicting a method of performing a cement operation with expandable cement, in accordance with an embodiment of the disclosure; and

FIGS. 5-7 are graphs illustrating various outputs generated by the cement design tool, in accordance with an embodiment of the disclosure.

DETAILED DESCRIPTION OF THE INVENTION

The description that follows includes exemplary apparatus, methods, techniques, and instruction sequences that embody techniques of the inventive subject matter. However, it is understood that the described embodiments may be practiced without these specific details.

The disclosure relates to a method for performing cement operations involving designing a cement for use in wellsite applications. The method may be used, for example, to design expandable cement based on design parameters of the wellsite operation. The design parameters may relate to specified downhole conditions, such as wellbore geometries, stiffness of casing and/or formations and downhole temperature/pressure changes.

The method may involve determining cement parameters, such as expansion eigenstrains (internal strains generated by an expanding agent of the cement), and designing the cement based on a correlation of the eigenstrains to downhole conditions. A model may be used to predict the effects of external loads and geometrical constraints on the magnitude and anisotropy-degree of the eigenstrains induced by expanding agents in the cement. Using this model, the cement-expansion determined from an unconfined expansion test may be correlated with the cement expansion in the downhole conditions. Expandable cement that is based on specified downhole conditions may then be designed. Various optional cements may be tested using expansion test apparatus. Expansion tests of various cements may be performed to select the desired cement and validate the cement.

FIGS. 1A and 1B illustrate a wellsite 100 in which the subject matter of the present disclosure may be employed. FIG. 1A depicts a drilled version of the wellsite 100. FIG. 1B depicts the wellsite 100 after completion. The wellsite 100 may be onshore or offshore, and may have a variety of wellsite equipment 110 positioned thereabout to perform various operations.

In the drilled example wellsite 100 of FIG. 1A, a wellbore 102 may be formed in subsurface formations by rotary drilling using any suitable technique. The wellsite 100 is provided with wellsite equipment 110 including a platform and derrick assembly 112 positioned over the wellbore 102. A drill string 104 may be suspended from the assembly 112 and advanced into the wellbore 102. The drill string 104 may have a bottom hole assembly (BHA) 106 that includes a drill bit 108 at its lower end.

In the wellsite system 100 of FIG. 1A, the wellsite equipment 110 may also include drilling fluid (or mud) 114 stored in a pit 116 formed at the well site. A pump 118 may deliver the drilling fluid 114 to the interior of the drill string 102 via the assembly 112, causing the drilling fluid to flow downwardly through the drill string 102 as indicated by the directional arrows. The drilling fluid 114 may exit the drill string 102 via ports in the drill bit 108, and circulate upwardly through an annulus between an outside of the drill string 102 and a wall of the wellbore 102, as indicated by the directional arrows. In this manner, the drilling fluid 114 lubricates the drill bit 108 and carries formation cuttings up to the surface, as the fluid 114 is returned to the pit 116 for recirculation.

The BHA 106 may include various components used in drilling, such as a logging-while-drilling (LWD) module 116, a measuring-while-drilling (MWD) module 118, a roto-steerable system and motor 120, and a telemetry device 122. The LWD and MWD modules 116, 118 may be employed to obtain various downhole measurements and/or wellbore parameters. The telemetry device 122 may be used for communication with on or off site locations, such as surface unit 124.

The surface unit 124 may be positioned about the wellsite 100 to perform various operations, such as collecting data, processing data, providing reports, and/or operating the wellsite 100. As shown, the surface unit 124 includes a cement tool 126 to collect data from the wellsite and to determine wellsite, downhole, cement and/or other parameters. The surface unit 124 and/or cement tool 126 may be used to generate various outputs, such as the graphs of FIGS. 5-7 as are described further herein.

The surface unit 124 may include any desired combination of hardware and software. For example, a personal computer platform, workstation platform, etc. may store on a computer readable medium, for example, a magnetic or optical hard disk, or random access memory, and execute one or more software routines, programs, machine readable code, or instructions to perform the operations described herein. Additionally or alternatively, the surface unit 124 may utilize dedicated hardware or logic such as, for example, application specific integrated circuits, configured programmable logic controllers, discrete logic, analog circuitry, or passive electrical components to perform the functions or operations described herein.

Still further, the surface unit 124 may be positioned proximate or adjacent to the wellsite equipment 110. Part or all of the entire surface unit 124 may be operationally and communicatively coupled to the wellsite equipment 110 (e.g., telemetry device 122) via any combination of one or more wireless or hardwired communication links (not shown in the drawings, which may be via a packet switched network (e.g., the Internet), hardwired telephone lines, cellular communication links, or other radio frequency based communication links which may utilize any communication protocol as known to one of ordinary skill in the art). The BHA 106 may also include one or more processors or processing units (not shown in the drawings).

As shown in FIG. 1B, the drill string 104 has been removed and a casing 136 is deployed into the wellbore 102 and cemented in place by cement 138. One or more casings 136 may be provided in the wellbore 102. The cement 138 is pumped into the wellbore 102 by a cementing tool 140 deployed into the wellbore 102, and coupled to a cement source 142 at the surface. The cement 138 may be in liquid form when deployed from the cement source 142 into the wellbore 102, and solidify over time within the wellbore 102.

As shown, the cement 138 is positioned between the casing 136 and the wall of the wellbore 102, but may be positioned at any location along the wellbore 102. For example, the cement 138 may be placed in an annular gap between casings, between casing and formation, and/or in other locations about the wellbore 102. Cement may be used, for example, to prevent casing corrosion, to provide mechanical strength, to prevent fluid communication, and/or to ensure zonal isolation.

The cement may include various components usable for providing various effects at the wellsite 100. The cement may be formed of a slurry with additives with various properties that provide various cementing functions. For example, expandable cements may include expanding agents to prevent the formation of microannuli along the wellbore. Examples of usable cements are described in US Patent No. 20110193564, previously incorporated by reference herein. The hydration of expanding agents may generate at a given pre-stress level along the wellbore. The pre-stress may be determined from expansion measurement(s), downhole conditions and wellbore parameters.

Microannuli form, for example, between the casing and the cement (inner microannulus) and/or between the cement and the formation (outer microannulus). Inner microannulus may be caused, for example, by radial displacement of the casing resulting from wellbore temperature/pressure changes (or other factors). Outer microannulus may be caused, for example, by bulk-shrinkage of cement. Microannuli may provide a leakage pathway for migration of downhole fluid resulting in a loss of zonal isolation.

Expanding agents may be used, for example, to hydrate and crystallize in late stages of cement hydration. As a result, a volume of cement may increase and compressive forces may buildup inside the cement and along cement/formation and cement/casing interfaces. A magnitude of expansion may depend on cement parameters, such as the expanding agent, cement powder, slurry design, wellbore conditions, confinement conditions, and/or curing conditions. In cases where expansion may not be sufficient, microannuli may form and the cement may not properly seal the wellbore.

FIGS. 2A-2B show various configurations of a cement expansion apparatus usable for measuring cement parameters of the cement 138 (FIG. 1) under unconfined conditions. FIG. 2A schematically shows an unconfined expansion tester 244.1 in an operational position coupled to the cementing tool 126. FIG. 2B shows the unconfined expansion tester 244.1 in an open position.

The unconfined expansion tester 244.1 includes a split ring body 246.1, a removable lid 248.1, and sensor 250.1. The split ring body 246.1 has an expansion chamber 249.1 therein to receive cement for expansion testing. The sensor 250.1 includes two pins 247.1 positioned about a periphery of the split ring body 246.1 to detect movement thereof. The lid 248.1 may be disposed on the split ring body 246.1. This configuration may provide for axial isolation of the cement in the ring body 246.1 and allow for unconfined expansion of the cement along radial and circumferential directions.

The sensor 250.1 may be used to detect movement of the pins 247.1 as the cement expands within the expansion chamber 249.1. As the cement 138 hardens and expands within the ring body 246.1, the cement 138 applies a force that expands an outer surface of the ring body 246.1. The pins 247.1 move as the ring body 246.1 expands with the cement 138. A distance d between the pins 247.1 may be measured by sensor 250.1 and an associated expansion eigenstrain (internal strain generated by the expanding agent) determined.

The cement tool 126 may be used to generate an isotropic expansion eigenstrain from data collected from the sensor 250.1 of the unconfined expansion tester 244.1. The unconfined expansion tester 244.1 may be coupled to the cement tool 126 for receiving data from the sensor 250.1. Data from the cement tester 244.1 may also be input to the cement tool 126.

The cement tool 126 includes a processor 248, a database 250, and a communicator 252. The surface unit 124 may be coupled to the wellsite 100, the cement tester 244.1, and/or other sources. Data from various sources may be received directly or indirectly by database 250 and stored therein. In some cases, the cement tool 126 and the cement tester 244.1 may be used separately from the surface unit 124 and the wellsite 100.

The communicator 252 may be coupled to the various sources, such as the cement tester 244.1, and used to transfer signals (e.g., data and/or communication) between the cement tool 126, cement tester 244.1, wellsite 100, and/or other sources. Data is collected in the database 250. Data receivable by the database 250 may be received from the sensors 250.1, the wellsite 100, historical data, user input, etc. The processor 248 may be used to sort, process, manipulate, and/or analyze the data. The processor 248 may also be used to perform calculations (e.g., modeling, determining parameters) and/or generate outputs based on the data received.

FIGS. 3A-3B show another cement expansion apparatus usable for measuring cement parameters of the cement 138 under confined conditions. FIG. 3A schematically shows a confined expansion tester 244.2 in an operational position coupled to the cementing tool 126. FIG. 3B shows a schematic view of operation of the confined expansion tester 244.2. The confined expansion tester 244.2 includes a ring body 246.2 and sensors 250.2. The ring body has an expansion chamber 249.2 defined between inner ring 251 and outer ring 253 to receive cement for expansion testing.

The sensors 250.2 are positioned about an inner surface of the inner ring 251 and an outer surface of the outer ring 253 to detect movement thereof. As shown three sensors 250.2 are positioned at various locations on each of the inner ring 251 and the outer ring 253. Leads 255 are shown coupled to the sensors 250.2 and the cement tool 126. The confined expansion tester 244.2 and sensors 250.2 may be coupled to the cement testing tool 126 using the leads 255 and/or in the same way as described with respect to the cement tester 244.1.

The inner ring 251 has an external radius R extending from a center of the confined expansion tester 244.2. The outer ring has an inner radius r1 and an outer radius r2 extending from the center of the confined expansion tester 244.2. The external radial confinement is defined by the thickness of the outer ring by r2-r1. The confined expansion tester 244.2 provides a radially confined configuration with the inner ring 251 and outer ring 253 deformable during expansion. Such deformation may be detectable by the sensors 250.2 to determine confined expansion of the cement 138 therebetween.

The cement tool 126 may be used to receive signals from the sensors 250.2 and generate anisotropic expansion eigenstrains (internal strains generated by the expanding agent) from the cement tester 244.2. The expandable cement may be placed in the expansion chamber 249.2 between the inner ring 251 and outer ring 253. Water in excess may be placed in the expansion chamber 249.2 on top of the cement. When the cement starts expanding, stresses may progressively develop due to radial confinement. Resulting circumferential strains J1 and J2 may be measured with the sensors 250.2 (e.g., strain gauges) respectively along the inner surface of inner ring 251 and the outer surface of the outer ring 253. The J1 and J2 provide empirical strains used to determine empirical expansion eigenstrains.

The cement testers 244.1, 244.2 may be used to measure the empirical strains to generate certain empirical measurements (e.g., empirical expansion eigenstrain(s)) of the cement and/or to perform a variety of tests, such as an unconfined or confined expansion test, on a sample of a given cement. These measurements may be determined using, for example, the relationship as set forth in Equations (2) and (3) described below. The cementing tool 126 may be used to determine cement parameters, such as expansion eigenstrain(s) (internal strain(s) generated by the expanding agent of the cement 138) from the tests.

The cement parameters may be evaluated to determine operability under wellsite conditions. The cementing tool 126 may be used to collect cement parameters and wellsite information to determine a desired configuration of the cement to meet requirements of a given wellsite. For example, the cementing tool 126 may be used to determine the magnitude of expansion eigenstrain(s) of a cement sample tested by the cement testers 244.1, 244.2.

The expansion eigenstrain(s) induced by expanding agents may, in contrast to thermal expansion, be affected by external loading conditions or geometrical constraints. For example, the overall volume expansion may be reduced for cylindrical cement specimens confined laterally. Theoretical analysis and physical models may demonstrate effects of external load on the orientation of crystallization for expanding agents. These models may involve a detailed knowledge on microstructure of cement, such as pore volume and pore-size distribution.

Examples relating to cement and/or expansion eigenstrain analysis are provided in Axel-Pierre Bois, Curis Tec, André Gamier, Grégory Galdiolo, and Jean-Benoît Laudet (2012), Use of a Mechanistic Model To Forecast Cement-Sheath Integrity, SPE Drilling & Completion, Volume 27, Number 2, SPE 139668; Hobbs D. W., (1988), Alkali-silica in Concrete, Thomas Telford, London; Le Roux A., Massieu E., Godart B. (1992), Evolution Under Stress of Concrete Affected by A.A.R—Application to Feasibility of Strengthening a Bridge by Prestressing, 9th International Conference on Alkali-Aggregate Reaction, Londre, p. 599-606; Larive C., Laplaud A., Joly M., (1996) Behavior of AAR-Affected Concrete: Experimental Data, 10th International Conference on Alkali-Aggregate Reaction, Melbourne, Australia, p. 670-677; Multon S., Toutlemonde F., (2006), Effect of Applied Stress on Alkali-silica Reaction-Induced Expansion, Cem. Con. Res., vol. 36, p. 912-920; Lecampion, B. (2010) Stress-Induced Crystal Preferred Orientation in the Poromechanics of In-pore Crystallization, J. Mech. Phys. Solids, Vol. 58. 1701-1715; and Lou, Y., Bassani, J., (2010), Effects of Elastic Interactions on Aggregation of Nanostructures, Acta Materialia, 58(17), 5654-5666, the entire contents of which are hereby incorporated by reference herein.

FIG. 4 is a flow chart depicting a method 400 of performing a cement operation using expandable wellbore cement, such as the cement 138 usable at wellbore 100 (FIG. 1B). The method 400 involves 460—determining design parameters of the wellbore (e.g., wellbore geometry, confinement, and pre-stresses of the wellbore). The design parameters may include a minimum pre-stress of the wellbore sufficient to prevent creation of a microannulus in the wellbore.

The method may also involve 462—determining an estimated eigenstrain of the expandable cement based on the design parameters (the estimated unconfined expansion eigenstrain sufficient to generate the minimum pre-stress determined), 464—selecting an expandable cement based on the estimated eigenstrain, and 466—validating the selected expandable cement by comparing the estimated experimental eigenstrain with the empirical eigenstrain.

The determining 460 design parameters may involve determining a variety of parameters, such as wellbore geometry, confinement, and pre-stresses of the wellbore. The wellbore parameters may relate to wellbore conditions that may affect which cement to use. For example, the selected cement may be provided with cement parameters that adapt to the pre-stress needs of the wellbore. Risk factors, such as possible casing movement and downhole temperature/pressure changes, wellbore geometries and stiffness of casing/formation as inputs, may determine the magnitude of pre-stress that is required to prevent the formation of a microannulus along the wellbore.

Pre-stress may be determined by solving different thermo-mechanical problems which simulate wellbore scenarios the cement may encounter. For each potential wellbore scenario, a cementing location in the wellbore may include at least one casing, cement, and layers of formation. This cementing location may be subject to pressure and temperature loading at its boundaries, representative of a wellbore operation. In addition, an initial isotropic compressive stress state (or pre-stress) may be assumed inside the cement. The combination of this pre-stress and the loading may induce a debonding at a cement/casing interface or cement/formation interface.

The cement may be designed to prevent the failure along these interfaces. Governing equations for the temperature T and stress fields σ are given by:

$\begin{matrix} {\frac{\partial T}{\partial t} = {D{\nabla^{2}T}}} & {{Equation}\mspace{14mu} (1)} \\ {{\nabla{\cdot \sigma}} = 0} & {{Equation}\mspace{14mu} (2)} \\ {\sigma = {C \cdot \left( {ɛ \cdot ɛ^{T}} \right)}} & {{Equation}\mspace{14mu} (3)} \end{matrix}$

where ε and ε^(T) are total strain and thermal strain, respectively, D is the thermal diffusivity, and C is the stiffness tensor.

For each scenario, the initial stress state may vary (starting from zero) until the chosen pre-stress value provides a final state without de-bonding at interfaces. The minimum pre-stress may be determined from the stress state that ensures no microannuli are generated in even a worst case scenario.

The determining 462 may involve estimating the unconfined expansion eigenstrain necessary to generate the minimum pre-stress based on the design parameters, such as the wellbore geometry and confinement of the worst case scenario. The determining 462 may involve determining the magnitude and anisotropy-degree of expansion eigenstrains (i.e., how the eigenstrain in radial direction is different than that in circumferential direction) under the confinement conditions considered. The confined expansion eigenstrains may be determined based on wellbore geometries and stiffness of casing/formation as inputs. The determining 462 may also involve correlating anisotropic expansion eigenstrains under downhole confinement conditions to the isotropic eigenstrain under unconfined condition.

The determining 462 may be performed using modeling techniques. A model may be used to correlate the anisotropic eigenstrains under downhole confinement conditions to the isotropic expansion eigenstrain under unconfined conditions. The associated pre-stress may be calculated by adding the expansion eigenstrain tensor or anisotropic eigenstrain tensor E^(T) similarly to thermal eigenstrain tensor in the linear elastic stress-strain relationship of the cement that is given by Equation (3).

The model may be used to predict the anisotropic eigenstrains of expandable cement as a function of the expansion eigenstrain under unconfined conditions, external loads and geometrical constraints. The estimated eigenstrains generated by the expanding agents, defined as ε_(ij) ^(T) may be isotropic when no external loads or geometrical constraints are applied to a cement sample. Therefore, under unconfined condition, the eigenstrain can be expressed as follows:

$\begin{matrix} {ɛ_{ij}^{T} = {ɛ_{0}^{T}\begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}}} & {{Equation}\mspace{14mu} (4)} \end{matrix}$

The magnitude of the eigenstrain under unconfined expansion condition,

may be measured using, for example, the unconfined expansion tester 244.1 of FIGS. 2A and 2B.

Due to the external loads and constraints of casing/formation, the eigenstrain tensor of expandable cement becomes anisotropic, which can be expressed as:

$\begin{matrix} {ɛ_{ij}^{T}\begin{pmatrix} ɛ_{rr}^{T} & 0 & 0 \\ 0 & ɛ_{\theta\theta}^{T} & 0 \\ 0 & 0 & ɛ_{zz}^{T} \end{pmatrix}} & {{Equation}\mspace{14mu} (5)} \end{matrix}$

where each estimated eigenstrain ε^(T) is presented with respect to the radial (r), circumferential θ, and axial directions z. Principle irections for the estimated eigenstrains may be assumed to be coincident with cylindrical coordinates of the wellbore. Values of each of the eigenstrains ε_(rr) ^(T), ε_(θθ) ^(T), and ε_(zz) ^(T) may depend on external loading conditions.

External load that is on the order of up to about hundreds of megapascal in a given oil-field application may have little effect on the kinetics of hydration and crystallization of expanding agents. Such loading conditions may have an effect on orientation of crystallization. For example, crystal may tend to aggregate in directions with less compressive load. A phenomenological form to relate eigenstrains ε_(rr) ^(T), ε_(θθ) ^(T) and ε_(zz) ^(T) with unconfined expansion eigenstrain ε_(o) ^(T) is introduced:

(ε_(rr) ^(T))²+(ε_(θθ) ^(T))²+(ε_(zz) ^(T))²=α(ε_(o) ^(T))²  Equation (6)

where α is a constant energy coefficient that can be estimated with experiments.

Using this relation, the values of ε_(rr) ^(T), ε_(θθ) ^(T) and ε_(zz) ^(T) may be obtained by minimizing an objective energy function inside of the cement-sheath. An objective energy function may include: i) the total elastic energy given by Equation (7), ii) the shear strain energy given by Equation (8), and hydrostatic strain energy given by Equation (9). Depending on different cement formula, the objective energy may be determined from the following:

$\begin{matrix} {W_{elastic} = {\int{\frac{1}{2}\sigma_{ij}\sigma_{ij}{V}}}} & {{Equation}\mspace{14mu} (7)} \\ {W_{shear} = {\int{\frac{1}{2}S_{ij}S_{ij}{V}}}} & {{Equation}\mspace{14mu} (8)} \\ {W_{hydro} = {\int{\frac{1}{3}\sigma_{0}^{2}{V}}}} & {{Equation}\mspace{14mu} (9)} \end{matrix}$

where σ is the total stress, S_(ij) is the deviatoric part of the stress, and σ₀ is the hydrostatic part of the stress inside the cement.

The stress state inside the cement may depend on design parameters, such as geometries of wellbore and/or the stiffness of casing/formation. Stress fields of cement-sheath that arise from anisotropic expansion eigenstrains may be calculated. The estimated eigenstrains and associated unconfined eigenstrains may be calculated using, for example, CEMSTRESS™ software commercially available from SCHLUMBERGER TECHNOLOGY CORPORATION™ at www.slb.com.

The selecting 464 an expandable cement may involve identifying a certain cement based on the determining 460, 462. More than one potential cement may be selected. A specified expandable cement that meets the design parameters (e.g., required expansion eigenstrain and/or pre-stress sufficient to prevent microannuli) may be selected by adjusting the concentration of expanding agent, cement formula, water to cement ratio and other parameters.

Using design parameters (e.g., cement/casing stiffness, geometry) and values generated from the confined expansion tester 244.2, the anisotropic eigenstrains ε_(rr) ^(T) and ε_(θθ) ^(T) of the cement may be estimated. The cement may be selected based on various parameters, such as different cement components, geometry of the confined expansion tester 244.2, and stiffness of casing and/or formations.

The validating 466 may be performed to assure that the selected cement meets wellsite operational needs and/or requirements. The validating 466 may involve 468—performing expansion tests on the selected expandable cement, and 470—confirming that the selected expandable cement meets the design parameters (e.g., pre-stress).

The performing 468 may involve performing 468.1 an unconfined expansion test on a design cement sample using the unconfined expansion tester of FIGS. 2A-2B. The unconfined expansion eigenstrain may be confirmed, for example, by measuring expansion under unconfined conditions of the selected cement to verify that the selected cement meets requirements. If not, a new cement may be selected until the requirements are met.

The performing 468 may also involve performing 468.2 a confined expansion test on a design cement sample using the confined expansion tester 244.2 of FIGS. 3A-3B. The confined anisotropic eigenstrains may be confirmed, for example, by measuring expansion under confined conditions of the selected cement to verify that the selected cement meets requirements. If not, a new cement may be selected until the requirements are met.

In the expansion experiment under confined conditions depicted in FIGS. 3A-3B, the calculated anisotropic eigenstrains ε_(rr) ^(T) and ε_(θθ) ^(T), which are based on strain-gauge measurements may be compared with the isotropic eigenstrain ε_(o) ^(T) measured with the unconfined expansion tester 244.1. FIG. 5 is a graph 500 depicting a comparison of the isotropic eigenstrain measured from the unconfined expansion tester 244.1 and the anisotropic eigenstrains measured from the confined expansion tester 244.2. The graph 500 depicts expansion eigenstrains (y-axis) versus case number (CN) (x-axis) for different unconfined estimated eigenstrains ε_(o) ^(T) and experimental eigenstrains for comparison. Under annular geometry of the confined expansion tester 244.2, the eigenstrains may be anisotropic and significantly different than the isotropic eigenstrain generated by the unconfined expansion tester 244.1.

The estimated anisotropic eigenstrains modeled using the unconfined expansion eigenstrain and equation (6) and (7-9) may be compared with those obtained by using experimental measurements of the confined expansion apparatus 244.2. FIG. 6 is a graph 600 depicting a comparison of these estimated and experimental expansion eigenstrains. The graph 600 depicts expansion eigenstrain % (y-axis) versus case number (CN) (x-axis) of the experimental eigenstrains and the estimated eigenstrains for comparison. FIG. 7 is a graph 700 depicting microstrain (y-axis) versus case number (CN) (x-axis) of associated experimental and modeled inner and outer micro strains J1 and J2 for comparison. The modeling results may be in agreement with experimental results of the testers 244.1, 244.2.

The validation and adjustment of eigenstrains may be used to reduce inconsistency between modeling and experiments, defined as follows:

|ε_((exp)) ^(T)−ε_((model)T)|  Equation (10)

Referring back to FIG. 4, the method may also involve measuring design parameters, performing empirical testing, deploying the validated cement into the wellbore, completing the wellbore with the validated cement, and collecting wellsite data. The methods may be performed in any order, and repeated as desired.

While the embodiments are described with reference to various implementations and exploitations, it will be understood that these embodiments are illustrative and that the scope of the inventive subject matter is not limited to them. Many variations, modifications, additions and improvements are possible. For example, expansion of the cement may be measured, calculated, and/or validated using a variety of techniques, such as those provided herein, and combinations thereof.

Plural instances may be provided for components, operations or structures described herein as a single instance. In general, structures and functionality presented as separate components in the exemplary configurations may be implemented as a combined structure or component. Similarly, structures and functionality presented as a single component may be implemented as separate components. These and other variations, modifications, additions, and improvements may fall within the scope of the inventive subject matter.

Although the preceding description has been described herein with reference to particular means, materials and embodiments, it is not intended to be limited to the particulars disclosed herein; rather, it extends to all functionally equivalent structures, methods and uses, such as are within the scope of the appended claims. 

What is claimed is:
 1. A method of performing a cementing operation with an expandable cement deployable into a wellbore penetrating a subterranean formation, the method comprising: determining design parameters of a wellsite, the design parameters comprising a minimum pre-stress of the wellbore sufficient to prevent creation of a microannulus in the wellbore; determining at least one estimated eigenstrain of the expandable cement based on the design parameters, the at least one estimated eigenstrain sufficient to generate the determined minimum pre-stress; selecting the expandable cement based on the at least one estimated eigenstrain; and validating the selected expandable cement by comparing the at least one estimated eigenstrain with the at least one empirical eigenstrain.
 2. The method of claim 1, further comprising performing at least one expansion test to generate the at least one empirical eigenstrain.
 3. The method of claim 2, wherein the at least one expansion test comprises at least one of an unconfined expansion test, a confined expansion test, and combinations thereof.
 4. The method of claim 2, wherein the performing comprises determining at least one isotropic eigenstrain using an unconfined expansion tester.
 5. The method of claim 2, wherein the at least one expansion test comprises determining at least one anisotropic eigenstrain tensor of the at least one empirical eigenstrain using a confined expansion tester.
 6. The method of claim 1, wherein the at least one estimated eigenstrain and the at least one empirical eigenstrain are unconfined.
 7. The method of claim 1, wherein the at least one estimated eigenstrain and the at least one empirical eigenstrain are confined.
 8. The method of claim 1, wherein the at least one empirical eigenstrain comprises an eigenstrain tensor, the eigenstrain tensor comprising a magnitude of anisotropy and a degree of anisotropy.
 9. The method of claim 1, further comprising measuring the at least one empirical eigenstrain using a cement expansion apparatus.
 10. The method of claim 9, wherein the cement expansion apparatus comprises one of an unconfined expansion tester, a confined expansion tester, and combinations thereof.
 11. The method of claim 1, further comprising selecting a new expandable cement when the at least one empirical eigenstrain is outside a pre-defined range of the at least one estimated eigenstrain.
 12. The method of claim 11, further comprising repeating the selecting and validating until the at least one empirical eigenstrain is within a pre-defined range of the at least one estimated eigenstrain for the new expandable cement.
 13. The method of claim 1, further comprising cementing the wellbore using the validated expandable cement.
 14. The method of claim 1, wherein the determining comprises measuring at least one of the design parameters at the wellbore.
 15. The method of claim 1, wherein the design parameters comprise wellbore geometry, casing stiffness, wellbore stiffness, and combinations thereof.
 16. A method of performing a cementing operation with an expandable cement deployable into a wellbore penetrating a subterranean formation, the method comprising: designing an expandable cement for cementing the wellbore, the designing comprising: determining design parameters of a wellsite, the design parameters comprising a minimum pre-stress of the wellbore sufficient to prevent creation of a microannulus in the wellbore; determining at least one estimated eigenstrain of the expandable cement based on the design parameters, the at least one estimated eigenstrain sufficient to generate the determined minimum pre-stress; selecting the expandable cement based on the at least one estimated eigenstrain; and validating the selected expandable cement by comparing the at least one estimated eigenstrain with the at least one empirical eigenstrain; and cementing the wellbore with the designed expandable cement.
 17. The method of claim 16, further comprising securing a casing in the wellbore with the cement.
 18. The method of claim 16, further comprising lining a portion of the wall of the wellbore with the cement.
 19. The method of claim 16, wherein the cementing comprises completing the wellbore using the designed expandable cement.
 20. A method of performing a cementing operation with an expandable cement deployable into a wellbore penetrating a subterranean formation, the method comprising: measuring at least one estimated eigenstrain of at least one expandable cement with at least one cement expansion apparatus; designing an expandable cement for cementing the wellbore, the designing comprising: determining design parameters of a wellsite, the design parameters comprising a minimum pre-stress of the wellbore sufficient to prevent creation of a microannulus in the wellbore; determining at least one estimated eigenstrain of the expandable cement based on the design parameters, the at least one estimated eigenstrain sufficient to generate the determined minimum pre-stress; selecting the expandable cement based on the at least one estimated eigenstrain; and validating the selected expandable cement by comparing the at least one estimated eigenstrain with the at least one empirical eigenstrain.
 21. A system of performing a cementing operation with an expandable cement deployable into a wellbore penetrating a subterranean formation, the method comprising: a cement expansion apparatus comprising an expandable body with sensors thereon, the expandable body having a cement cavity therein, the sensors positionable about the expandable body to measure expansion thereof; and a cement tool operatively connectable to the cement expansion apparatus, the cement tool comprising a database to receive data from the cement expansion apparatus and a processor to determine cement parameters from the data whereby expansion of the cement is determinable thereby.
 22. The system of claim 21, wherein the cement tool is operatively connectable to a wellsite, the database to receive data from the wellsite and the processor to determining cement parameters from the data whereby cement parameters for cement operations are determinable thereby.
 23. The system of claim 21, wherein the cement expansion apparatus comprises one of a confined expansion tester having a split ring configuration and an unconfined expansion tester having a dual ring configuration. 